8h^2-84h+76=0

Solution for 8h^2-84h+76=0 equation:

Simplifying
8h2 + -84h + 76 = 0

Reorder the terms:
76 + -84h + 8h2 = 0

Solving
76 + -84h + 8h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '4'.
4(19 + -21h + 2h2) = 0

Factor a trinomial.
4((1 + -1h)(19 + -2h)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + -1h)' equal to zero and attempt to solve:

Simplifying
1 + -1h = 0

Solving
1 + -1h = 0

Move all terms containing h to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1h = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1h = 0 + -1
-1h = 0 + -1

Combine like terms: 0 + -1 = -1
-1h = -1

Divide each side by '-1'.
h = 1

Simplifying
h = 1
Subproblem 2
Set the factor '(19 + -2h)' equal to zero and attempt to solve:

Simplifying
19 + -2h = 0

Solving
19 + -2h = 0

Move all terms containing h to the left, all other terms to the right.

Add '-19' to each side of the equation.
19 + -19 + -2h = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -2h = 0 + -19
-2h = 0 + -19

Combine like terms: 0 + -19 = -19
-2h = -19

Divide each side by '-2'.
h = 9.5

Simplifying
h = 9.5
Solution
h = {1, 9.5}